Related papers: Probabilistic consequence relations
We survey some results that provide different versions of classical results through different summability methods. Specifically, in order to adapt such classical results, we analyze which properties should satisfy the summability methods.…
Two interpretations about syllogistic statements are described in this paper. One is the so-called set-based interpretation, which assumes that quantified statements and syllogisms talk about quantity-relationships between sets. The other…
This paper gives a generative model of the interpretation of formal logic for data-driven logical reasoning. The key idea is to represent the interpretation as likelihood of a formula being true given a model of formal logic. Using the…
We study the interplay between sequential decision making and avoiding discrimination against protected groups, when examples arrive online and do not follow distributional assumptions. We consider the most basic extension of classical…
Probabilistic independence is a useful concept for describing the result of random sampling---a basic operation in all probabilistic languages---and for reasoning about groups of random variables. Nevertheless, existing verification methods…
This paper is concerned with the paraconsistent first-order logic LPQ$^{\supset,\mathsf{F}}$, Priest's LPQ enriched with an implication connective and a falsity constant. A sequent-style natural deduction proof system for this logic is…
In this paper we explore the application of methods for classical judgment aggregation in pooling probabilistic opinions on logically related issues. For this reason, we first modify the Boolean judgment aggregation framework in the way…
Through extended consideration of two wide classes of case studies -- dilute gases and linear systems -- I explore the ways in which assumptions of probability and irreversibility occur in contemporary statistical mechanics, where the…
Possibilistic logic offers a qualitative framework for representing pieces of information associated with levels of uncertainty of priority. The fusion of multiple sources information is discussed in this setting. Different classes of…
Recent published work has addressed the Shalqvist correspondence problem for non-distributive logics. The natural question that arises is to identify the fragment of first-order logic that corresponds to logics without distribution, lifting…
There is much interest in providing probabilistic semantics for defaults but most approaches seem to suffer from one of two problems: either they require numbers, a problem defaults were intended to avoid, or they generate peculiar side…
The main result presented in this article is that probability can fundamentally be characterized as a subset of conditional expectation induced by a plausible preorder on random quantities. This is justified by the fact that probability is…
Autoregressive Large Language Models (LLMs) trained for next-word prediction have demonstrated remarkable proficiency at producing coherent text. But are they equally adept at forming coherent probability judgments? We use probabilistic…
We systematically investigate the complexity of model checking the existential positive fragment of first-order logic. In particular, for a set of existential positive sentences, we consider model checking where the sentence is restricted…
We present a semantics for adding uncertainty to conditional logics for default reasoning and belief revision. We are able to treat conditional sentences as statements of conditional probability, and express rules for revision such as "If A…
The well-studied notion of deductive explosion describes the situation where any formula can be deduced from an inconsistent set of formulas. Paraconsistent logic, on the other hand, is the umbrella term for logical systems where the…
We present a semantics of a probabilistic while-language with soft conditioning and continuous distributions which handles programs diverging with positive probability. To this end, we extend the probabilistic guarded command language…
In finite probability theory, events are subsets of the outcome set. Subsets can be represented by 1-dimensional column vectors. By extending the representation of events to two dimensional matrices, we can introduce "superposition events."…
To operate intelligently in the world, an agent must reason about its actions. The consequences of an action are a function of both the state of the world and the action itself. Many aspects of the world are inherently stochastic, so a…
At the onset of quantum mechanics, it was argued that the new theory would entail a rejection of classical logic. The main arguments to support this claim come from the non-commutativity of quantum observables, which allegedly would…